# zbMATH — the first resource for mathematics

A minimal predicative set theory. (English) Zbl 0816.03023
The authors choose a very weak set theory, denoted by N, having just the following axioms: (1) $$\emptyset$$ exists, and (2) for any two sets $$x$$, $$y$$, $$x\cup \{y\}$$ exists, and prove that Robinson’s arithmetic Q is interpretable in N. This is to be understood as a reasonable reduction from the point of view of Hilbert’s Program, which continues analogous work of E. Nelson. The proof of the interpretability of Q into N is given through a large number of steps which are a bit difficult to follow. A finistic proof of Herbrand consistency of N is also given.

##### MSC:
 3e+70 Nonclassical and second-order set theories
Full Text: